SOLUTION: lnx-3/lnx=-2

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Question 1119321: lnx-3/lnx=-2
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
As it is written and presented, it is UNREADABLE.


Is it   ln(x) - (3/ln(x)) = -2     or

        (ln(x)-3)/ln(x) = - 2     or

        ln(x-3)/ln(x) = - 2     ? ? ?


To make it readable,  use parentheses properly and systematically.


Primitive  "copy and paste"  DOES NOT WORK,  when you post formulas to this forum !



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(NOTE: The use of parentheses WOULD be preferable. However, using standard rules for interpreting the equation as you show it produces only one meaning.)

ln%28x%29-3%2Fln%28x%29=-2

Multiply both sides by ln(x) to get a "quadratic" in ln(x):

%281n%28x%29%29%5E2-3+=+-2ln%28x%29
%28ln%28x%29%29%5E2%2B2ln%28x%29-3+=+0
%28ln%28x%29%2B3%29%28ln%28x%29-1%29+=+0
ln%28x%29+=+-3 or ln%28x%29+=+1
x+=+e%5E-3 or x+=+e

CHECK...

x = e: ln%28e%29-3%2Fln%28e%29+=+1+-+3%2F1+=+-2 yes

x = e^-3: ln%28e%5E-3%29-3%2Fln%28e%5E-3%29+=+-3+-+%283%2F-3%29+=+-3%2B1+=+-2 yes